Child’s Apple ID

Follow the steps here: link-> Create an Apple ID for your child - Apple Support

To create an Apple ID for a child under 13 , you will need an Apple device.

If you create a regular Apple Id for and age of 13 or over, you can create it directly on your granddaughter's iPhone and yes, sign out from your own.

I would, if the iPhone has been backed up, and does not have a ton of info yet associated with your Apple ID, then just restore it to factory condition, and set it up again. Then create the Apple ID during setup, instead of using your own.

See here: link-> Restore your iPhone, iPad, or iPod to factory settings - Apple Support

then here: link-> Set up your iPhone, iPad, or iPod touch - Apple Support

and here: link-> How to create a new Apple ID - Apple Support

You are welcome. When she has her own ID, you will sign out of your ID on her phone, and she will sign in with her ID.

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. If possible, also set up Family Sharing  between the IDs to keep access to your apps/purchases. 

 How to switch Apple IDs on your iPhone or iPad.      

How to transfer all files from one iCloud account to another.       

What to do after you change your Apple ID or password - Apple Support.      

Family Sharing.         

Family Sharing - Set up.        

Deleting your Apple ID account won't make it any easier to set up the child's account. Can you borrow an Apple device/computer to try to set up the child's ID?

You are welcome.